{
  "abstract": "Learning by confusion (LBC) is a machine-learning method for locating phase transitions without assuming a known order parameter. Its characteristic accuracy curve contains a central maximum that is interpreted as the transition point, but what determines the location and finite-size scaling of this maximum has remained unclear. We derive an exact balance condition for the Bayes-optimal confusion peak and show that, for equilibrium systems with a single swept parameter, the peak closely follows the maximum of the corresponding Fisher information. This immediately gives its finite-size scaling and reveals an unexpected dependence on how the data are sampled: the same configurations arranged on grids uniform in $T$, $\\ln T$, or $β=1/T$ can yield different finite-size pseudocritical trajectories. Tests on the Ising, Blume-Capel, Potts, and Baxter-Wu models confirm the prediction across continuous, tricritical, and first-order transitions. Our results identify the statistical quantity measured by LBC and show that finite-size machine-learning estimates can depend on the parametrization of the training data as well as on the underlying physics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34769",
  "author_total": 2,
  "authors": [
    {
      "name": "George Issa"
    },
    {
      "name": "Richard Scalettar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3nczzrz9fqxeq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34769",
  "fulltext_url": null,
  "id": "3nczzrz9fqxeq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34769",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "physics.data-an"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7223796519",
  "pdf_url": "https://arxiv.org/pdf/2610.34769",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3nczzrz9fqxeq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.34769",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34769"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Learning by Confusion Locates a Parametrization-Dependent Fisher Information Maximum",
  "title_text": "Learning by Confusion Locates a Parametrization-Dependent Fisher Information Maximum",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:21Z",
  "url": "https://research.draconitic.com/paper/3nczzrz9fqxeq",
  "venue": "arXiv",
  "versions": []
}